On the combinatorics of sparsification
Fenix W. D. Huang, Christian M. Reidys

TL;DR
This paper analyzes the combinatorial aspects of sparsification in RNA folding algorithms, showing significant theoretical and experimental reductions in computational complexity for various energy models.
Contribution
It introduces a combinatorial framework to quantify sparsification effects in RNA structure folding, including expected candidate set sizes and complexity reductions.
Findings
Sparsification reduces RNA folding time complexity by up to 98%.
The framework predicts candidate set sizes using probabilistic models.
Experimental results confirm theoretical complexity reductions.
Abstract
Background: We study the sparsification of dynamic programming folding algorithms of RNA structures. Sparsification applies to the mfe-folding of RNA structures and can lead to a significant reduction of time complexity. Results: We analyze the sparsification of a particular decomposition rule, , that splits an interval for RNA secondary and pseudoknot structures of fixed topological genus. Essential for quantifying the sparsification is the size of its so called candidate set. We present a combinatorial framework which allows by means of probabilities of irreducible substructures to obtain the expected size of the set of -candidates. We compute these expectations for arc-based energy models via energy-filtered generating functions (GF) for RNA secondary structures as well as RNA pseudoknot structures. For RNA secondary structures we also consider a simplified…
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Taxonomy
TopicsRNA and protein synthesis mechanisms · RNA modifications and cancer · Bacterial Genetics and Biotechnology
